scholarly journals A Fourier Approach for the Level Crossings of Shot Noise Processes with Jumps

2012 ◽  
Vol 49 (01) ◽  
pp. 100-113 ◽  
Author(s):  
Hermine Biermé ◽  
Agnès Desolneux
Keyword(s):  
Shot Noise ◽  
Poisson Point Process ◽  
Functions Of Bounded Variation ◽  
Level Crossing ◽  
Level Crossings ◽  
Variable Formula ◽  
Shot Noise Process ◽  
Change Of Variable ◽  
The Mean ◽  
The Fourier Transform

We use a change-of-variable formula in the framework of functions of bounded variation to derive an explicit formula for the Fourier transform of the level crossing function of shot noise processes with jumps. We illustrate the result in some examples and give some applications. In particular, it allows us to study the asymptotic behavior of the mean number of level crossings as the intensity of the Poisson point process of the shot noise process goes to infinity.

scholarly journals A Fourier Approach for the Level Crossings of Shot Noise Processes with Jumps

2012 ◽  
Vol 49 (1) ◽  
pp. 100-113 ◽  
Author(s):  
Hermine Biermé ◽  
Agnès Desolneux
Keyword(s):  
Shot Noise ◽  
Poisson Point Process ◽  
Functions Of Bounded Variation ◽  
Level Crossing ◽  
Level Crossings ◽  
Variable Formula ◽  
Shot Noise Process ◽  
Change Of Variable ◽  
The Mean ◽  
The Fourier Transform

We use a change-of-variable formula in the framework of functions of bounded variation to derive an explicit formula for the Fourier transform of the level crossing function of shot noise processes with jumps. We illustrate the result in some examples and give some applications. In particular, it allows us to study the asymptotic behavior of the mean number of level crossings as the intensity of the Poisson point process of the shot noise process goes to infinity.

On hitting times for compound Poisson dams with exponential jumps and linear release rate

2001 ◽  
Vol 38 (3) ◽  
pp. 781-786 ◽  
Author(s):  
Offer Kella ◽  
Wolfgang Stadje
Keyword(s):  
Release Rate ◽  
Shot Noise ◽  
Hypergeometric Functions ◽  
Hitting Times ◽  
Stieltjes Transform ◽  
Compound Poisson ◽  
Confluent Hypergeometric Functions ◽  
Kummer Functions ◽  
Shot Noise Process ◽  
The Mean

For a compound Poisson dam with exponential jumps and linear release rate (shot-noise process), we compute the Laplace-Stieltjes transform (LST) and the mean of the hitting time of some positive level given that the process starts from some given positive level. The solution for the LST is in terms of confluent hypergeometric functions of the first and second kinds (Kummer functions).

On hitting times for compound Poisson dams with exponential jumps and linear release rate

2001 ◽  
Vol 38 (03) ◽  
pp. 781-786 ◽  
Author(s):  
Offer Kella ◽  
Wolfgang Stadje
Keyword(s):  
Release Rate ◽  
Shot Noise ◽  
Hypergeometric Functions ◽  
Hitting Times ◽  
Stieltjes Transform ◽  
Compound Poisson ◽  
Confluent Hypergeometric Functions ◽  
Kummer Functions ◽  
Shot Noise Process ◽  
The Mean

For a compound Poisson dam with exponential jumps and linear release rate (shot-noise process), we compute the Laplace-Stieltjes transform (LST) and the mean of the hitting time of some positive level given that the process starts from some given positive level. The solution for the LST is in terms of confluent hypergeometric functions of the first and second kinds (Kummer functions).

scholarly journals On the intensity of crossings by a shot noise process

1987 ◽  
Vol 19 (3) ◽  
pp. 743-745 ◽  
Author(s):  
Tailen Hsing
Keyword(s):  
Shot Noise ◽  
Marginal Probability ◽  
Noise Process ◽  
Shot Noise Process

The crossing intensity of a level by a shot noise process with a monotone response is studied, and it is shown that the intensity can be naturally expressed in terms of a marginal probability.

Inequalities for the M/G/∞ queue and related shot noise processes

1987 ◽  
Vol 24 (04) ◽  
pp. 978-989 ◽  
Author(s):  
Fred W. Huffer
Keyword(s):  
Poisson Process ◽  
Shot Noise ◽  
Convex Functions ◽  
Sample Path ◽  
Noise Process ◽  
Shot Noise Process

Suppose that pulses arrive according to a Poisson process of rate λ with the duration of each pulse independently chosen from a distribution F having finite mean. Let X(t) be the shot noise process formed by the superposition of these pulses. We consider functionals H(X) of the sample path of X(t). H is said to be L-superadditive if for all functions f and g. For any distribution F for the pulse durations, we define H(F) = EH(X). We prove that if H is L-superadditive and for all convex functions ϕ, then . Various consequences of this result are explored.

scholarly journals Survey-based Impact of Influencing Parameters on Level Crossings Safety

2016 ◽  
Vol 28 (6) ◽  
pp. 639-649 ◽  
Author(s):  
Martin Starčević ◽  
Danijela Barić ◽  
Hrvoje Pilko
Keyword(s):  
Survey Questionnaire ◽  
Level Crossing ◽  
Level Crossings ◽  
Policy Makers ◽  
Railway Traffic ◽  
Research Activities ◽  
On Line ◽  
Line Survey ◽  
First Time ◽  
Influential Parameters

Level crossing (LC) accidents are a significant safety challenge worldwide and for that reason they have been subject of numerous research activities. Joint conclusion is that human behaviour is the main cause of accidents. This study examines how and to which extent certain influential parameters cause accident mechanisms on level crossings. To gain the necessary data we used an on-line survey questionnaire that was sent internationally to key experts in the field of road and railway safety. A total of 185 experts were asked to rank how much certain parameters influence level crossings accident mechanisms and what are the best countermeasures for diminishing accidents at level crossings. To our knowledge, this is the first time that an international survey among key experts was used to gain necessary data about influential parameters regarding level crossings safety. The results of this study could be used by road and railway traffic engineers and policy makers for further enhancement of LC’s safety.

scholarly journals Study of Drivers’ Behaviour at a Passive Railway Crossing

1970 ◽  
Vol 24 (3) ◽  
pp. 193-201 ◽  
Author(s):  
Sandra Kasalica ◽  
Radisav Vukadinović ◽  
Vojkan Lučanin
Keyword(s):  
Observational Study ◽  
Road Traffic ◽  
Level Crossing ◽  
Level Crossings ◽  
Road Vehicle ◽  
Railway Crossing ◽  
Limited Visibility ◽  
Risky Decisions

Problem: The number of killed and injured persons in incidents at railway level crossings is generally increasing on the Serbian Railways, particularly at passive crossings. In this paper we researched the direct behaviour of road traffic participants at a conventional railway passive crossing. Method: Direct observational study of drivers’ behaviour at a level crossing. Results: Sixty-one road vehicle drivers were observed in the moments of train approach. The probability of crossing varies depending on the train distance and the time the driver has to cross the crossing. The drivers who have limited visibility cannot estimate the speed of the approaching train well and make more risky decisions. Conclusion: This study shows that the number of “risky crossings” is worrying as the result of such crossings is a large number of accidents with fatal consequences at the passive crossings in Serbia.

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